## Introduction

The congested wireless spectrum and its continued reallocation require future radar systems to be both adaptive and reconfigurable. To date, 3.45 GHz to 3.7 GHz from the United States S-band radar allocation has been re-allocated for sharing between radar and wireless communications, with a recent ruling allocating the 3.45 GHz to 3.55 GHz to fifth-generation (5G) wireless communications as the primary user [1]. The 3.55 GHz to 3.7 GHz band has been allocated for sharing between radar, the Citizens Band Radio Service (CBRS) [2], and the 4G and 5G wireless transmissions [2]. Additionally, the 3.1 to 3.45 GHz subband has also been proposed for sharing [3]. The use of a phased array enables the radar transmitter to perform directional and potentially multiple-beam transmissions to increase spectrum efficiency. Transmitter arrays must be able to reconfigure quickly, changing direction and beam pattern to coexist with communications in this band.

Recent development of high-power reconfigurable circuit technology suitable for radar use [4] has made possible the concept of reconfigurable transmitter amplifiers. Using reconfigurable power amplifiers as building blocks within the array elements, real-time optimizations of array power-amplifier circuitry, phase shifts, and excitation waveforms are needed to maximize the sharing of finite spectral and spatial resources. AI and ML are expected to be useful in successfully and efficiently combining these multi-parameter, multi-objective optimizations. While typical prior applications of AI in radar have been limited to target tracking and recognition, control and enhanced performance, and signal processing and synthesis; the further application of AI and ML to optimizing transmission waveforms, circuits, and arrays in an AIPAA will allow performance to be optimized when changing operating frequency or scan angle in a spectrum sharing environment.

## AIPAA

A block diagram of the AIPAA is shown in Fig. 1. The AIPAA must perform a multi-objective optimization to achieve the goals of range, power efficiency, and spectral and spatial containment.

The AIPAA will contain the ability to re-match its power amplifiers "on the fly" with reconfigurable matching networks. This will allow power to be optimized on transmission, which maximizes the range of the transmission, while also maximizing the power-added efficiency (PAE) and meeting spectral and spatial constraints. Single-element circuit optimization techniques must be expanded to allow multi-amplifier optimizations in the array. Qiao demonstrates adaptive power-amplifier matching in traditional microwave-band transmissions [5]. Semnani has demonstrated a 90-W RF power handling impedance tuner designed for radar transmissions in the S-band from 3.1 to 3.5 GHz [4].

In the AIPAA, the input waveforms and phase shifting should be adjusted in concert with the impedance tuners in each element to meet the aforementioned multiple objectives. Eventually, each "element" may move physically throughout a specified geographic area, potentially changing the array configuration.

## Real-Time Impedance Tuning

The
use of amplifier load-impedance reconfiguration for use in arrays has
been explored by Rodriguez-Garcia for single- and dual-beam array
transmission [6], [7].
The tuning of an amplifier’s load impedance can affect the range and
the spectral mask compliance of the transmission. A single-element
experiment by Alcala-Medel [8]
shows a three-frequency reconfiguration measurement experiment from
which the calculated range (based on measured output power) and measured
spectral mask compliance were plotted against measurement number, as
shown in Fig. 2.
Since a radar application was envisioned in this reference, the radar
range was calculated from the measured output power using assumed radar
system parameters. The spectral mask metric *S _{m}* is defined such that mask compliance is obtained for

*S*≤ 0 [9]. Fig. 2 shows that the range is reduced upon changing frequency without re-tuning (visible at measurements 12 and 25). At measurement 12 where the system changes from 3.3 GHz to 3.1 GHz, the

_{m}*S*value goes up from 0 to almost 2, transitioning from compliance to significant non-compliance. Re-tuning allows both the range and spectral mask compliance to be improved/restored after shifting to 3.1 GHz. Similar effects occur upon the shift to 3.5 GHz, followed by improvements resulting from impedance tuning. While Rodriguez-Garcia has shown that impedance tuning can reduce spurious emissions in arrays while maximizing element gain [7], such optimizations (to be performed in real time) will require global monitoring of the entire array and optimization of the entire system. Intelligent measurement, monitoring, optimization, and control techniques will be crucial. Techniques such as the

_{m}*in situ*impedance sensor designed by Donahue [10] will be useful in assessing system performance during optimization.

## Spatial-Spectral Mask for Coexistence

Because many radars use phased arrays, they have the capability to promote coexistence through directional transmission. We have suggested the use of a spatial-spectral mask for coexistence in directional transmissions, as introduced by Egbert [11]. If the maximum interference power received by each receiver in the geographic vicinity of a transmitter is made available, then the needed spatial-spectral mask to preserve coexistence can be calculated using the Friis transmission equation. Fig. 3 shows an example of the spatial-spectral mask. The spatial-spectral mask can be used as a constraint in an optimization routine that maximizes quality of service [11].

If the maximum interference spatial-spectral power density tolerable by each device *P _{r}*(

*f*,

*R*,

*ϕ*) is known based on its frequency

*f*, and its radius

*R*and angle ∅ from the transmitter, then the power that can be transmitted per Hz bandwidth and per radian angle is shown in [11] to be given, based on the Friis equation, by

Egbert also shows that, given a transmission pattern *G _{t}*(

*ϕ*), a spectral power density constraint map can be derived, given by [11] as:

Similarly, for a given a normalized transmission spectrum *X*(*f*), a spatial power density constraint map can be derived, also shown in [11]:

Given the spectral mask requirements that can be generated based on a known transmission pattern, waveform optimization can be used to obtain a desired ambiguity function, while meeting the spectral mask constraints derived from the spectral/spatial mask constraints. An example was given by Egbert [11] that shows the development of a range-oriented radar for an ideal beam steered to a center angle of 60° with a beam width of 30°, over which the transmission is isotropic. Fig. 4 shows the ambiguity function template, which minimizes the ambiguity away from the Doppler axis (Fig. 4(a)), along with the ambiguity function of the achieved waveform (Fig. 4(b)). The spectrum of the optimized waveform is shown with the spectral mask in Fig. 4(c) [11]. As expected for a range-oriented radar, the waveform optimization results in a waveform with wide bandwidth that meets the spectral mask constraints.

A similar situation is expected to exist for the application of the spatial mask, using a given waveform. The array will be optimized to obtain desired beamforming characteristics, but will be subjected to the spatial mask constraints created based on the frequency content of the waveform.

In the AIPAA system, joint optimization of the waveform, array, and circuit is desired to maximize all objectives simultaneously. The concept of merging optimizations must be addressed in detail in the future. First efforts toward optimization merging are explained in the next section.

## Joint Optimizations

Merging the optimizations of the circuit, array, and waveform to achieve a defined multi-objective success is a key challenge of the AIPAA. A reasonable first step toward this challenge is to combine optimizations of the different parameters in small steps. As an example of combining two disparate optimizations, we present the joining of optimizations of a radar transmitter circuit with that of the waveform, as presented by Latham [12]. A gradient-based circuit optimization was interwoven with an ambiguity-function based waveform optimization. Each waveform optimization iteration was assumed to require only one-fifth of the time of an impedance tuning iteration. To depict this scenario, a sequence of five waveform optimization steps, followed by one circuit optimization step, was performed. The overall optimization seeks to match the radar range/Doppler ambiguity function to a template while maximizing the PAE and meeting spectral mask constraints. Fig. 5 shows a block diagram of the joint circuit and waveform optimization procedure.

Fig. 6 shows a comparison of the joint (one circuit iteration followed by five waveform iterations) and sequential (complete circuit optimization followed by complete waveform optimization) optimizations [12]. The sequential optimization (Fig. 6(a)) (which completely optimizes the circuit first) results in a quick rise in PAE. However in Fig. 6(b), a corresponding very large least-squares distance from the ambiguity-function template results for the first half of the sequential search, indicating poor range/Doppler ambiguity function performance of the transmitted waveform. The joint optimization provides gradual raising of PAE to its final value, and a much better (lower) least-squares distance through the entire search, indicating a radar waveform with more desirable resolution. Fig. 6(c) shows that the spectral mask limitations are also reached more quickly in the joint optimization, because the desired high-bandwidth waveform appears earlier in the search. Joint optimization allows a compromise of all objectives to be reached in a quicker manner.

To illustrate the benefit of using joint optimization to ensure all objectives are optimized quickly, Fig. 7 shows the ambiguity function of the measured waveforms for the joint and sequential optimizations at equivalent waveform iteration 26 (an iteration of the circuit optimization accounts for 5 equivalent waveform iterations) [12]. The ambiguity function from the joint optimization shows good agreement with the template, while the ambiguity function from the sequential optimization (the circuit is optimized first) does not show good agreement with the template. This corresponds with the large disparity in least-squares distance between the joint circuit and waveform optimizations visible in Fig. 6(b) for a value of 26 on the horizontal axis.

The AIPAA requires joint optimizations of the circuit, waveform, array excitations (including phase shifts) and possibly the array element positions. As the numbers of objectives and parameters are increased, AI and ML are expected to increase their roles in making joint optimizations efficient. These searches will likely be framed as multi-objective and constrained optimizations, and domain expertise should be used to enhance learning algorithms for application to the AIPAA. While AI and ML can be useful if they fit the context to which they are applied, blindly using AI to try to sort out optimization problems is a dangerous pitfall. Trendy AI techniques, such as Deep Convolutional Neural Networks, and Reinforcement Learning, while potentially useful in certain scenarios, have significant limitations. Such techniques should be used only in applications for which they are designed.

## Effect of Impedance Tuning on Array Pattern

The effects of impedance tuning on array patterns are less widely documented in the literature than the effects of impedance tuning on the spectrum. However, since the linearity of the transmitter power amplifier depends significantly on its load impedance, the load impedance influences the array pattern fidelity through the linearity (or nonlinearity) of the power amplifier. As two-tone spectra can be used to show the generation of nonlinear intermodulation products through the nonlinear amplifier’s creation of two (or more) additional tones, the input of two beam kernels to a power amplifier results in the creation of two (or more) additional unwanted beams to be generated [13], [14]. In general, a combined spectral-spatial intermodulation can occur from a dual-beam, dual-tone transmission, as shown by Hemmi [15] and Haupt [16].

Since it has been shown that nonlinearities in the power amplifier can cause unwanted beam effects; it stands to reason that impedance tuning, which can be used to linearize the power amplifier, can be used to provide a cleaner beam pattern in the same manner used to provide a clean transmission spectrum. Rodriguez-Garcia demonstrates the use of impedance tuning to maximize power-amplifier gains in the individual elements of an array, while increasing the beam pattern fidelity, both in single-beam [6] and dual-beam [7] cases.

Moving
forward, these optimizations should be integrated with real-time
evaluation measurements. Real-time array optimization algorithms must be
created that allow efficient optimization of impedance tuners in the
array elements. These optimizations will rely on real-time *in situ*
measurements that are capable of measuring critical elements to
determine the spatial distortion and the gain values of the individual
amplifiers. The development of *in situ* measurement techniques, such as an impedance sensor recently demonstrated by Donahue [10], that can be used in the array elements is a high priority in developing this technology.

Given the benefits of impedance tuning in cleaning transmissions in both the spectral and spatial domain, the combined optimization approach joining circuit and waveform optimization of Latham [12] must be extended to envelop the spatial domain as well. The growing complexity of this optimization problem suggests that AI and ML, utilizing domain expertise, may be useful tools if appropriately applied.

## Conclusions

The AIPAA will merge array, circuit, and waveform optimizations for successfully sharing spectrum resources with users in directional transmissions, such as 5G Long Term Evolution mmW communications and array radar systems. Use of a joint spectral and spatial mask in constraining optimizations and an approach for joining optimizations have been described as useful techniques for constraining and merging optimizations in the AIPAA.

### ACKNOWLEDGMENTS

Parts of this work were funded by the National Science Foundation (Grant No. ECCS-1343316) and the Army Research Laboratory (Grant No. W911NF-16-2-0054). The views and opinions expressed do not necessarily represent the opinions of the U.S. Government.